Master Solving Absolute Value Equations with Extraneous solutions

The video tutorial explains how to solve absolute value equations, focusing on cases with variables on both sides and the importance of checking for extraneous solutions. It covers isolating absolute values and solving complex equations, providing step-by-step guidance and examples to ensure understanding.

What is the first step in solving an absolute value equation with variables on both sides?

• Divide both sides by a variable

• Add the same number to both sides

• Isolate the absolute value

• Multiply both sides by a constant

Why is it important to check for extraneous solutions in absolute value equations?

• To ensure the equation is balanced

• To verify the solution satisfies the original equation

• To simplify the equation further

• To find the maximum value of the variable

When can you create two cases for an absolute value equation?

• When the absolute value is isolated

• When the equation is linear

• When the equation has no variables

• When the equation is quadratic

What is a common mistake when solving absolute value equations?

• Forgetting to add a constant to both sides

• Not isolating the absolute value before creating cases

• Dividing by a variable

• Multiplying both sides by zero

How do you handle an equation where the absolute value is not isolated?

• Add a constant to both sides

• Subtract the variable from both sides

• Use inverse operations to isolate the absolute value

• Multiply both sides by a constant

What should you do after solving an absolute value equation?

• Check the solution in the original equation

• Multiply the solution by a constant

• Add the solution to both sides

• Divide the solution by a variable

In the final example, what is the correct solution for the equation 9 - 2X = 10 + 3X?

• X = -3

• X = 2

• X = -1/5

• X = 1

What is the result of checking the solution X = -19 in the final example?

• It balances the equation

• It simplifies the equation

• It is an extraneous solution

• It is a valid solution

What is the main goal before creating two cases in an absolute value equation?

• To multiply both sides by a variable

• To add a constant to both sides

• To isolate the absolute value

• To simplify the equation

What is the importance of checking solutions in absolute value equations?

• To simplify the equation

• To balance the equation

• To ensure no extraneous solutions

• To find the maximum value